Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决,你就会知道这些概率密度看上去的样子。
If you didn't come to New York, maybe you'd live in Puerto Rico. What would your life be like?
如果你没有来纽约,或许你会住在波多黎各。那么,你生活会怎么样?
This is your opportunity, if you're sitting at home, you could take off to turn off the TV.
机会来了,如果你正在家里,就可以马上开始了,关上电视。
If you don't do that, there's a danger you will learn something you don't have to, and we don't want that.
但是如果你不来,你就有可能学到一些不重要的知识,我们当然不希望这样
Then you might--well let me ask you this, what would happen if Google decided to buy up all of its shares?
你也可能,我来问问你,如果谷歌决定购回它所有的股票会怎么样呢
But you can also look at it qualitatively, so, if you think about the force between the electron and the proton, you could just qualitatively think about what's happening.
但你也可以定性的来研究这个问题,所以如果你们考虑电子,和质子之间的作用力,你可以定性的来想。
You've all been immunized for Hepatitis B, would you be happy to hear that that's where your Hepatitis B vaccine came from?
你们都对乙型肝炎具有免疫力了,如果你知道你的乙型肝炎疫苗,是从何而来的话,你还会高兴的起来吗
Instead of looking at the documents from the outside, let's look at what would an early Christian church look like if you were just to stumble upon them? A little imagination.
这次我们不再客观地看文本,我们来看看一个早期基督教会的样子,如果你无意间进了教会,想象一下。
And, if you ever get confused, the way to remember these is that you know energy is the integral of a force moving through a distance.
如果你感到很困惑的话,可以这么来记,能量是在沿力的方向进行路径积分。
So this program, if you run it based on intuition or little cheat sheets in front of you, what is this program ultimately going to do for me?
所以这个程序,如果你按照你的直觉,或你们面前的备忘单来执行它,这个程序最终会为我做什么?
Since then, since we know about atoms and molecules now, we can rationalize the concepts of thermodynamics using microscopic properties, 62 and if you are going to take 5.62, that's what you'd learn about.
既然我们现在已经知道了原子和分子,的概念),我们可以用,微观属性,来阐释热力学中的概念,如果你会选修5。,-那是你将要学到的。
You can sign up with the Salem Fire Corporation, pay a yearly subscription fee, and if your house catches on fire, they will come and put out the fire.
你可以和塞伦消防公司签约,每年支付会员费,如果你的房子着火,他们会来灭火。
If you have a dog and you say "Good dog" to reward the dog, by your logic, which is right, at some point you might as well give the dog a treat along with the "Good dog."
如果你有只狗,你用“好狗狗“这话来奖励它,根据你正确的逻辑,总有时候你会在说“好狗狗“的同时,给它些奖励“
And basically if you phone them up, you get a taxi that comes and picks you up,
基本上,如果你给他们打电话,就有出租车来接你,
And the reason I want to show you this is to notice that the recursion can be doubled.
如果我来写斐波那契数列你可以看看这儿,原因是我想让你看看这部分的递归可以翻倍。
There's a line that I'm going to be developing, pushing, if you will, or defending in this class.
我用一条线来表示,如果你愿意推动或者保护这个课题。
Namely, it's going to happen this summer, because we're coming and it's going to happen this week; it's going to happen tomorrow, if you don't run away.
就是说今年夏天就会发生,因为我们来入侵了,本周也可能发生,如果你不逃走,明天就会发生
If it's more affordable of course you'd want to use an economic intervention.
如果是因为价格便宜,你可能会想到通过经济干预来解决
So, in particular, let's start working out what share of the votes you'd get if you chose position 1 or position 2, against different positions the other guy can choose.
先来看看如果你选择立场1和2,在你对手选择不同立场时,你分别能获得多少选票
It's much more a question of reminding you ; that if you can do it with this, you can do it with anything; but also of reminding you that, after all, reading--reading just anything--is a complex and potentially almost unlimited activity.
选择它主要是为了告诉你们,如果你能用理论来分析这篇,那么分析任何一篇都没问题;,还想提醒大家,阅读任何文章都是个复杂的过程,其中有无限种可能。
You throw out little slips of paper and they take turns going back and forth.
你如果将竞价写在纸上,他们会来来回回地传阅。
So if you want to spend some money, this is the right place to go.
所以,如果你愿意花一些钱,来这个地方就对了。
If you want to describe this particle, what's the kinematics?
如果你想描述这个质点,如何从运动学角度来描述呢
So, please don't bring in your attorney if I didn't ask a question that's identical to one that you've worked.
因此请不要带你的律师来,如果我没有考的题目,和你做过的题目相同的话。
Well, if you're implementing a computer that needs to represent information now all you need is something like electricity which can be on or off, on or off.
好吧,如果你正用一个电脑,来表现表达传递信息的功能,你就需要,像电开关一样的物体。
So technically, if you ask what does the velocity stand for-- Let me draw a general situation.
从学术角度来说,如果你问速度表示什么,那让我来给你画一个常见的场景
Others though, I want to tell you that it doesn't-- if you're shopping-- I had a student come by yesterday and ask he's a little rusty in his math skills if he should take this course.
其他的,我想告诉你们不必...,如果你还在挑选课程...,昨天有个学生来问我,他的数学有点荒废了,他该不该选这门课
And in terms of using these equations in solving problems on the exam, and also using these constants, make sure if you think there might be any chance you're going to get any little part of a problem wrong or do a calculation inaccurately, you need to write out every single step of your thinking as you write out these problems.
而当你在考试过程中用这些公式,来解题时,加上运用这些常数,如果你觉得有可能,在某一小问上出错,或者出现计算错误,请务必把你的思路一步一步地都写出来,当你在答题的时候。
So if it's not a cell that's going through division you can't use a retrovirus to express the protein.
如果细胞不在分裂阶段,你就不能用逆转录病毒来表达某个蛋白
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